The Mystery of Alpha and the Isotopes

We report unbiased AI measurements of the fine structure constant $\alpha$ in two proximate absorption regions in the spectrum of the quasar HE0515$-$4414. The data are high resolution, high signal to noise, and laser frequency comb calibrated, obtained using the ESPRESSO spectrograph on the VLT. The high quality of the data and proximity of the regions motivate a differential comparison, exploring the possibility of spatial variations of fundamental constants, as predicted in some theories. We show that if the magnesium isotopic relative abundances are terrestrial, the fine structure constants in these two systems differ at the 7$\sigma$ level. A 3$\sigma$ discrepancy between the two measurements persists even for the extreme non-terrestrial case of 100\% $^{24}$Mg, if shared by both systems. However, if Mg isotopic abundances take independent values in these two proximate systems, one terrestrial, the other with no heavy isotopes, both can be reconciled with a terrestrial $\alpha$, and the discrepancy between the two measurements falls to 2$\sigma$. We cannot rule out other systematics that are unaccounted for in our study that could masquerade as a varying alpha signal. We discuss varying constant and varying isotope interpretations and resolutions to this conundrum for future high precision measurements.